A: Excitedly B: Exhausted C: Either is fine Use "ly" when you are describing the action or verb. Don't use "ly" when you are describing the person or object which is taking the action. So, in A, you are not describing the catfish, you are describing the manner in which they swim, so you use "ly". In B, you are not describing "arrived", you are describing yourself when you arrived, so you do not use "ly". In the last one it doesn't matter because either your arrival was safe or you were safe when you arrived, and both mean the same thing in this case.

A: At present, scientists are studying catfish because they swim around excitedly just before an earthquake. B: I arrived home exhausted. C: I arrived home safely.